Recently, a new approach for eliminating interference at arrays has been presented that performs algebraic operations in which the interference, represented as vectors, is annihilated by a transformation into the zero vector. This represents a radically different approach from conventional methods commonly in use that employ beam-forming nulling (BFN). In such adaptive beam-forming (ABF) schemes, the interference is rejected by deliberately distorting the array beam pattern such that “nulls,” regions of markedly reduced array gain, are placed at those angles corresponding to the interference directions, which null out the interference. With the distortion of the beam pattern, the process of rejecting interference is accompanied unavoidably by distortion of the output signal time functions of interest, a problem associated with this technique, well known and largely ignored since its inception, and there are numerous applications in which this is especially undesirable. In radio astronomy, for example in the search for extraterrestrial intelligence (SETI), or in observations of pulsars or bursts and transients, preserving the properties and structure of the received time functions is essential. In communications systems and other applications such as guidance systems or aircraft landing systems, where accurate phase information is critical, signal distortion can be a very serious problem.
Algebraic Interference Cancellation (AIC) avoids the distortion in the beam patterns that occurs with conventional ABF. Briefly, any signal incident at an M-element array presents at each sampling instant a vector of M complex numbers. Consider vectors s and i representing a signal of interest and interference incident at an array. In AIC, a matrix A is constructed such that Ai=0. Consequently, the following relationship holds true: A(i+s)=As. Although in eliminating the interference the signal is transformed, the transformation by A is known exactly and can be reversed.
AIC avoids the signal distortion problem inherent in ABF by employing an algebraic operation consisting of a matrix multiplication whose effect on the signal of interest can be reversed, yielding an undistorted signal output. This represents a significant advantage of AIC over ABF. The weakness in AIC is that the vector i, that is, the direction of the interference, must be known in order to calculate the aforementioned matrix A. More specifically, AIC is an open-loop scheme in which the interference directions are determined in a step that is separate and independent from eliminating them. Although there are numerous algorithms in existence that can be used to identify angular locations of interfering sources, it would be desirable if the adaptive techniques employed with ABF could be used with AIC.